Ex 6.1,15 - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 6.1, 15 The total cost C(𝑥) in Rupees associated with the production of 𝑥 units of an item is given by 𝐶(𝑥) = 0.007𝑥^3 – 0.003𝑥2 + 15𝑥 + 4000. Find the marginal cost when 17 units are produced.Since Marginal Cost is Rate of change in Total Cost w.r.t No of units produced
Let MC be marginal cost
So, MC = 𝒅𝑪/𝒅𝒙
Given,
Total Cost = C(𝑥) =0.007𝑥^3−0.003𝑥^2+15𝑥+4000" "
We need to find marginal Cost when 17 units are produced
i.e. MC when 𝑥 = 17
MC = 𝑑(𝐶(𝑥))/𝑑𝑥
MC = 𝑑(0.007𝑥^3 − 0.003𝑥^2 + 15𝑥 + 4000)/𝑑𝑥
MC = 𝑑(0.007𝑥^3 )/𝑑𝑥 − 𝑑(0.003𝑥^2 )/𝑑𝑥+ 𝑑(15𝑥)/𝑑𝑥+ 𝑑(4000)/𝑑𝑥
MC = 0.007 𝑑(𝑥^3 )/𝑑𝑥 −0.003 𝑑(𝑥^2 )/𝑑𝑥 + 15𝑑(𝑥)/𝑑𝑥+0
MC = 0.007 × 3𝑥^2−0.003 ×2𝑥+15
MC = 0.021𝑥^2−0.006𝑥+15
We need to find MC when 𝑥=17
Putting 𝒙=𝟏𝟕
MC = 0.021(17)^2−0.006(17)+15
MC = 6.069 – 0.102 + 15
MC = 20.967
Hence, the Required Marginal cost is Rs. 20.967

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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